That was fast!
It's been less than 12 hours (I went to sleep and woke up with it fixed - on a Sunday, no less!)
GoDaddy has a reputation in the industry for excellent and professional customer service. They are also one of the few ISP's with a proper and formal DMCA process that is fair to all parties. If you are an ISP (especially one based in the US) you should have some sort of process like this - it helps stop you from being held partially responsible for the stolen information (it's on your servers, after all).
The Blue Time Media website no longer resolves to anything (screenshot below).
I've found that ISP's are often faster to respond to DMCA complaints than search engines, which is why it's part of my DMCA Complaint process. Blue Time Media has the opportunity to respond, of course, though it's really clear that this is not a grey issue (my name is actually on the pages they stole, and every page has a copyright notification on it, so they can't claim independent development, public domain, or anything like that).
I would like to thank GoDaddy for their response, and to take this opportunity to recommend them to my readers. If you are an honest webmaster, they are a great host to have!
Since I offer (limited) hosting myself, I'm technically a competitor, but that doesn't mean I don't appreciate professionalism and service when I see it. This is the second time I've dealt with an issue using GoDaddy. The first was not DMCA related - a client who hosted with them had some problems that were not GoDaddy's fault, but nonetheless the staff there solved for me quickly and efficiently.